The Principle's methodology seem to be fairly restrained and it's pretty obvious that the student knew he was in trouble and was trying to evade the Principal rather than just minding his own business and getting attacked. Whether the principal's actions were appropriate will depend on what led up to it (and possibly what happened in the little room out of camera view), but the Principal's actions that are seen on the video seemed to be well within the scope of his duty to maintain order in his school.